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Lynna [10]
4 years ago
7

Which is greatest 8/10, 9/10 or 3/4?

Mathematics
2 answers:
pogonyaev4 years ago
3 0
9/10 is the greatest of the three. 
lawyer [7]4 years ago
3 0
9/10 is the greatest than all of hem
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Find a formula for the least squares solution of ax=b when the columns of a are orthonormal1 .
neonofarm [45]
Let \mathbf A be a rectangular m\times n matrix with column vectors \mathbf a_1,\ldots,\mathbf a_n, i.e.

\mathbf A=\begin{bmatrix}\mathbf a_1&\cdots&\mathbf a_n\end{bmatrix}

Then we have

\mathbf A^\top=\begin{bmatrix}\mathbf a_1&\cdots&\mathbf a_n\end{bmatrix}^\top

and the product of the two is

\mathbf A^\top\mathbf A=\begin{bmatrix}\mathbf a_1\cdot\mathbf a_1&\mathbf a_1\cdot\mathbf a_2&\cdots&\mathbf a_1\cdot\mathbf a_n\\\mathbf a_2\cdot\mathbf a_1&\mathbf a_2\cdot\mathbf a_2&\cdots&\mathbf a_2\cdot\mathbf a_n\\\vdots&\vdots&\ddots&\vdots\\\mathbf a_n\cdot\mathbf a_1&\mathbf a_n\cdot\mathbf a_2&\cdots&\mathbf a_n\cdot\mathbf a_n\end{bmatrix}

Because the columns of \mathbf A are orthonormal, we have

\mathbf a_i\cdot\mathbf a_j=\begin{cases}1&\text{for }i=j\\0&\text{for }i\neq j\end{cases}

which means \mathbf A^\top\mathbf A reduces to an n\times n matrix with ones along the diagonal and zero everywhere else, i.e.

\mathbf A^\top\mathbf A=\begin{bmatrix}1&0&\cdots&0\\0&1&\cdots&0\\\vdots&\vdots&\ddots&\vdots\\0&0&\cdots&1\end{bmatrix}=\mathbf I_n

where \mathbf I denotes the identity matrix. This means the solution to \mathbf{Ax}=\mathbf b is given by

\mathbf A^\top(\mathbf{Ax})=\mathbf A^\top\mathbf b\implies(\underbrace{\mathbf A^\top\mathbf A}_{\mathbf I})\mathbf x=\mathbf A^\top\mathbf b\implies\mathbf x=\mathbf A^\top\mathbf b
6 0
3 years ago
The scale model of a skyscraper being built is 4.2 feet tall. When it is finished, the skyscraper will be 525 meters tall. What
luda_lava [24]
There are two scales that may be possible for this scale model; one where it's for every foot and one where it's for every meter.
The for every foot would be better to find out since the scale would be easier to use.
First, you have to divide each sided by 4.2, since you want to find how many meters for each foot.
4.2 \div 4.2 = 1 \\ 525 \div 4.2 = 125
For every 1 foot used in the model, the actual will be 125 meters.
1 ft = 125 m
8 0
3 years ago
Plz help! Is this right? Question is below!
ipn [44]

Answer:

first one im pretty sure

Step-by-step explanation:

5 0
4 years ago
What percent of 75 is 18.75
Murljashka [212]

Answer:

25%

Step-by-step explanation:

X=(18.75*100)/75

7 0
3 years ago
15 inches of snow fell in 12 hours. At this rate, how many inches of snow will fall in 3 days.
kirill [66]

Answer:

90 in

Step-by-step explanation:

15 x 6 = 90 in

This is because

6 x 12 hrs = 3 days

8 0
3 years ago
Read 2 more answers
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